Mathematics desk
< September 7	<< Aug \| September \| Oct >>	September 9 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

September 8

Need some literature about converting an exponential function to a linear representation

Need literature, above high-school level, but introductory. Given a function is in the form y = ax^2, and want to convert into a linear function, and plot it (i.e. log(y) = 2log(ax). Or function is in the form y = ax^2 + b and cannot apply the previous operation, but other means might be possible. Basically, how and when to convert into a linear function something that is exponential. --Yppieyei (talk) 12:04, 8 September 2015 (UTC)[reply]

Have you read Log–log_plot? You're not really changing the essence of the function, you're just changing the way you plot it. Or you could think of it as a mapping from functions of the form y=ax^2 to functions of the form Y=mX+b, via X=log(x). But the original function is still ~~exponential~~ nonlinear, and the target function is still ~~exponential~~ nonlinear in terms of x.

You might already know this, just wanted to link a relevant article. Is there something more specific you'd like to know? E.g. you can still plot y=ax^2+b on a log-log plot, and you can use List_of_logarithmic_identities#Summation.2Fsubtraction to handle the log of the sum if you want to do further algebraic manipulation. SemanticMantis (talk) 14:22, 8 September 2015 (UTC)[reply]

Log is a group homomorphism between the positive reals under multiplication and the reals under addition (i.e., log(ab)=log(a)+log(b)). If you want to get a sum of things after applying log, you should begin with a product of things. --JBL (talk) 14:52, 8 September 2015 (UTC)[reply]

Side note: If y = ax², then log(y) = log(a) + 2log(x). Only if y = (ax)², then log(y) = 2log(ax) = 2log(a) +2log(x). Abecedare (talk) 15:15, 8 September 2015 (UTC)\[reply]

Right, y = ax^2 and y = (ax)^2 are not the same.

I'm not just after a wikipedia article, even if these are good links, but published material. Something like [1], which would be an ideal choice, were it published yet. --Yppieyei (talk) 15:19, 8 September 2015 (UTC)[reply]